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How to Multiply Algebraic Fractions (Mathematics Lesson)

Multiplying Algebraic Fractions

Algebraic fractions can be multiplied.

Imagine you wanted to multiply ab and cd.

a over b times c over d

How to Multiply Algebraic Fractions

To multiply algebraic fractions, use the rule:

a over b times c over d equals a c over b d

A Real Example of How to Multiply Algebraic Fractions

An Example Question

Multiply the algebraic fractions below.

x over 2 times y over 3
Step 1

Compare the fractions you are multiplying with the rule shown above.

compare a over b times c over d and x over 2 times y over 3

By comparing, we see that a = x, b = 2, c = y, d = 3.

Step 2

Use the rule, with a = x, b = 2, c = y, d = 3:

a c over b d, replacing a with x, b with 2, c with y and d with 3
Step 3

Calculate the terms in the rule. Where we have written two numbers or letters in brackets together, multiply them together:

(x)(y) = x × y = xy

(2)(3) = 2 × 3 = 6

We have multiplied x2 and y3 together:

x over 2 times y over 3 equals x y over 6

Another Real Example of How to Multiply Algebraic Fractions

The slider below shows a real example of how to multiply algebraic fractions.

Interactive Test
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Here's a second test on multiplying algebraic fractions.
Here's a third test on multiplying algebraic fractions.

Note

Understanding the Rule

a over b times c over d equals a c over b d

Multiplying fractions requires:

  • multiplying the numerators together to form the numerator of the product...

    a times c equals a c
  • ... and multiplying the denominators together to form the denominator of the product:

    b times d equals b d

This gives the rule:

a over b times c times d equals a c over b d

The letters written next to each other denotes that they are multiplying each other.

The rule works when the a, b, c and d are numbers, letters, terms or expressions.

Make sure you can:

Top Tip

Cancelling Terms

When the numerator of one fraction equals the denominator of the other fraction, they cancel each other out:

Cancel out the b that is on the top and bottom of the fraction

This is how to simplify algebraic fractions.